Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
196 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20261623 | C2 | semidirect |
| 3. C4×#13095514 | C2 | semidirect |
| 5. #15690884 | C4 | direct (N × H) |
| 14. #13095514 | C2×C4 | semidirect |
| 43. C4×C97 | M32 | semidirect |
| 50. C97 | C4×M32 | semidirect |
| 93. C4 | #15690884 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690884 | 2 |
| #20261623 | 2 |
| C4×#13095514 | 2 |
| C2×C4×#11715895 | 2 |
| C4×M32 | 97 |